Dynamically generated logical qubits
Open accessAbstract
We present a quantum error correcting code with dynamically generated logical qubits . When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Our particular code gives a model very similar to the two-dimensional toric code, but each measurement is a t w o -qubit Pauli measurement.
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By picking an appropriate measurement schedule, each consisting of a set of 2-qubit measurements, one can actually encode two logical qubits dynamically in Kitaev's honeycomb code.
“We will show that by picking an appropriate measurement schedule, each consisting of a set of 2-qubit measurements, we can actually encode two logical qubits dynamically. This was discovered by Hastings and Haah in their seminal work [120] in 2021”
From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [120]
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Research works printed but not linked: 13
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- T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flens- berg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, "Scalable designs for quasiparticle- poisoning-protected topological quantum computation with majorana zero modes," Physical Re- view B 95, 235305 (2017), arXiv:1610.05289 . · DOI
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- B. Skinner, J. Ruhman, and A. Nahum, "Measurement-induced phase transitions in the dynamics of entanglement," Phys. Rev. X 9, 031009 (2019), arXiv:1808.05953 . · DOI
- M. J. Gullans and D. A. Huse, "Dynamical purification phase transition induced by quantum measurements," Physical Review X 10, 041020 (2020), arXiv:1905.05195 . · DOI
- A. Kitaev, "Anyons in an exactly solved model and beyond," Annals of Physics 321, 2-111 (2006), arXiv:cond-mat/0506438 . · DOI · Paper page
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- L. Fidkowski, J. Haah, and M. B. Hastings, "How dynamical quantum memories forget," Quantum 5, 382 (2021), arXiv:2008.10611 . · DOI
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“These properties have made it a leading contender in the design of fault tolerant quantum computers (though recently the competition has been growing [HH21; Bra+24; GJ23]).”
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Spencer, D. J., Jain, S. P., Tanggara, A., Sun, Z., Haug, T., Khu, D., & Bharti, K. (2026) · arXiv
- Authors
- Hastings, M. B., & Haah, J.
- Affiliations
- Microsoft (United States) (US)
- ORCID
- Haah, Jeongwan
- Venue
- Quantum
- Published
- 2021-10-19
- Volume
- 5
- Pages
- 564
- ISSN
- 2521-327X (ISSN-L)
- OpenAlex
- W3181439919
- Cited by
- 160
- References
- 0
- Citations by year
- 2026: 20 · 2025: 53 · 2024: 40 · 2023: 27 · 2022: 16 · 2021: 4
- FWCI
- 7.33
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum error correction, subsystem codes, fault-tolerant quantum memory, toric code, measurement patterns, logical qubits
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